{"id":965,"date":"2016-12-22T14:35:15","date_gmt":"2016-12-22T13:35:15","guid":{"rendered":"http:\/\/mathfinance.sns.it\/?p=965"},"modified":"2017-01-24T14:44:10","modified_gmt":"2017-01-24T13:44:10","slug":"schneider-m-and-lillo-f-2016-cross-impact-and-no-dynamic-arbitrage","status":"publish","type":"post","link":"http:\/\/mathfinance.sns.it\/index.php\/schneider-m-and-lillo-f-2016-cross-impact-and-no-dynamic-arbitrage\/","title":{"rendered":"Schneider, M. and Lillo, F. (2016) Cross-Impact and No-Dynamic-Arbitrage"},"content":{"rendered":"<p><strong>Abstract<\/strong><\/p>\n<p>We extend the \u201cNo-dynamic-arbitrage and market impact\u201d-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multidimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset i to asset j must be equal to the one from j to i. To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask spread.<\/p>\n<p><a href=\"https:\/\/ssrn.com\/abstract=2889029\">https:\/\/ssrn.com\/abstract=2889029<\/a><\/p>\n<p><a href=\"https:\/\/arxiv.org\/abs\/1612.07742\">https:\/\/arxiv.org\/abs\/1612.07742<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Abstract We extend the \u201cNo-dynamic-arbitrage and market impact\u201d-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multidimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can [&hellip;]<\/p>\n","protected":false},"author":17,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[11],"tags":[],"_links":{"self":[{"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/posts\/965"}],"collection":[{"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/comments?post=965"}],"version-history":[{"count":2,"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/posts\/965\/revisions"}],"predecessor-version":[{"id":967,"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/posts\/965\/revisions\/967"}],"wp:attachment":[{"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/media?parent=965"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/categories?post=965"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/mathfinance.sns.it\/index.php\/wp-json\/wp\/v2\/tags?post=965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}